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ACT
ACT Math Section

Minimizing Production Costs

Hard Modeling Applied Mathematics

A company is analyzing its production process for a new product. The total cost in dollars, $C$, of producing $x$ units of the product can be modeled by the equation:

$$C(x) = 500 + 20x + 0.1x^2$$

Where $500$ represents fixed costs, $20$ represents variable costs per unit, and $0.1$ represents the increasing marginal cost per unit produced. If the company wants to minimize its total cost, how many units should it produce?

Hint

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